**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**9531

# Search results for: sub-super solution method

##### 9531 A New Inversion-free Method for Hermitian Positive Definite Solution of Matrix Equation

**Authors:**
Minghui Wang,
Juntao Zhang

**Abstract:**

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

**Keywords:**
Inversion-free method,
Hermitian positive definite solution,
Maximal solution,
Convergence.

##### 9530 Analytical Solution for the Zakharov-Kuznetsov Equations by Differential Transform Method

**Authors:**
Saeideh Hesam,
Alireza Nazemi,
Ahmad Haghbin

**Abstract:**

This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.

**Keywords:**
Zakharov-Kuznetsov equation,
differential transform method,
closed form solution.

##### 9529 An Approximate Solution of the Classical Van der Pol Oscillator Coupled Gyroscopically to a Linear Oscillator Using Parameter-Expansion Method

**Authors:**
Mohammad Taghi Darvishi,
Samad Kheybari

**Abstract:**

In this article, we are dealing with a model consisting of a classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. The major problem is analyzed. The regular dynamics of the system is considered using analytical methods. In this case, we provide an approximate solution for this system using parameter-expansion method. Also, we find approximate values for frequencies of the system. In parameter-expansion method the solution and unknown frequency of oscillation are expanded in a series by a bookkeeping parameter. By imposing the non-secularity condition at each order in the expansion the method provides different approximations to both the solution and the frequency of oscillation. One iteration step provides an approximate solution which is valid for the whole solution domain.

**Keywords:**
Parameter-expansion method,
classical Van der Pol oscillator.

##### 9528 Two-Dimensional Solitary Wave Solution to the Quadratic Nonlinear Schrdinger Equation

**Authors:**
Sarun Phibanchon

**Abstract:**

The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.

**Keywords:**
soliton,
iterative method,
spectral method,
plasma

##### 9527 An Analytical Method for Solving General Riccati Equation

**Authors:**
Y. Pala,
M. O. Ertas

**Abstract:**

In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

**Keywords:**
Riccati Equation,
ordinary differential equation,
nonlinear differential equation,
analytical solution,
proper solution.

##### 9526 Constant Order Predictor Corrector Method for the Solution of Modeled Problems of First Order IVPs of ODEs

**Authors:**
A. A. James,
A. O. Adesanya,
M. R. Odekunle,
D. G. Yakubu

**Abstract:**

This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

**Keywords:**
Interpolation,
Approximate Solution,
Collocation,
Differential system,
Half step,
Converges,
Block method,
Efficiency.

##### 9525 Solution of Density Dependent Nonlinear Reaction-Diffusion Equation Using Differential Quadrature Method

**Authors:**
Gülnihal Meral

**Abstract:**

**Keywords:**
Density Dependent Nonlinear Reaction-Diffusion Equation,
Differential Quadrature Method,
Implicit Euler Method.

##### 9524 Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Clenshaw Method

**Authors:**
M. Saravi,
F. Ashrafi,
S.R. Mirrajei

**Abstract:**

**Keywords:**
Chebyshev polynomials,
Clenshaw method,
ODEs,
Spectral methods

##### 9523 Lagrangian Method for Solving Unsteady Gas Equation

**Authors:**
Amir Taghavi,
kourosh Parand,
Hosein Fani

**Abstract:**

In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.

**Keywords:**
Unsteady gas equation,
Generalized Laguerre functions,
Lagrangian method,
Nonlinear ODE.

##### 9522 Application of Homotopy Perturbation Method to Solve Steady Flow of Walter B Fluid A Vertical Channel In Porous Media

**Authors:**
A.Memari

**Abstract:**

In this article, a simulation method called the Homotopy Perturbation Method (HPM) is employed in the steady flow of a Walter's B' fluid in a vertical channel with porous wall. We employed Homotopy Perturbation Method to derive solution of a nonlinear form of equation obtained from exerting similarity transforming to the ordinary differential equation gained from continuity and momentum equations of this kind of flow. The results obtained from the Homotopy Perturbation Method are then compared with those from the Runge–Kutta method in order to verify the accuracy of the proposed method. The results show that the Homotopy Perturbation Method can achieve good results in predicting the solution of such problems. Ultimately we use this solution to obtain the other terms of velocities and physical discussion about it.

**Keywords:**
Steady flow; Walter's B' Fluid;,
vertical channel;porous media,
Homotopy Perturbation Method (HPM),
Numerical Solution (NS).

##### 9521 A Method for Improving the Embedded Runge Kutta Fehlberg 4(5)

**Authors:**
Sunyoung Bu,
Wonkyu Chung,
Philsu Kim

**Abstract:**

In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

**Keywords:**
Embedded Runge-Kutta-Fehlberg method,
Initial value
problem.

##### 9520 On the Solution of Fully Fuzzy Linear Systems

**Authors:**
Hsuan-Ku Liu

**Abstract:**

A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and Gauss- Seidel methods on approximating the solution of FFLS.

**Keywords:**
Fully fuzzy linear equations,
iterative method,
homotopy perturbation method,
approximate solutions.

##### 9519 Laplace Decomposition Approximation Solution for a System of Multi-Pantograph Equations

**Authors:**
M. A. Koroma,
C. Zhan,
A. F. Kamara,
A. B. Sesay

**Abstract:**

In this work we adopt a combination of Laplace transform and the decomposition method to find numerical solutions of a system of multi-pantograph equations. The procedure leads to a rapid convergence of the series to the exact solution after computing a few terms. The effectiveness of the method is demonstrated in some examples by obtaining the exact solution and in others by computing the absolute error which decreases as the number of terms of the series increases.

**Keywords:**
Laplace decomposition,
pantograph equations,
exact
solution,
numerical solution,
approximate solution.

##### 9518 Numerical Solution of Infinite Boundary Integral Equation by Using Galerkin Method with Laguerre Polynomials

**Authors:**
N. M. A. Nik Long,
Z. K. Eshkuvatov,
M. Yaghobifar,
M. Hasan

**Abstract:**

In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.

**Keywords:**
Approximation,
Galerkin method,
Integral
equations,
Laguerre polynomial.

##### 9517 Solution of Fuzzy Differential Equation under Generalized Differentiability by Genetic Programming

**Authors:**
N. Kumaresan,
J. Kavikumar,
M. Kumudthaa,
Kuru Ratnavelu

**Abstract:**

**Keywords:**
Fuzzy differential equation,
Generalized differentiability,
Genetic programming and H-difference.

##### 9516 Using Hermite Function for Solving Thomas-Fermi Equation

**Authors:**
F. Bayatbabolghani,
K. Parand

**Abstract:**

In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with solution of other methods that shows the present solution is more accurate and faster convergence in this problem.

**Keywords:**
Collocation method,
Hermite function,
Semi-infinite,
Thomas-Fermi equation.

##### 9515 Sinc-Galerkin Method for the Solution of Problems in Calculus of Variations

**Authors:**
M. Zarebnia,
N. Aliniya

**Abstract:**

**Keywords:**
Calculus of variation; Sinc functions; Galerkin; Numerical method

##### 9514 Non-Polynomial Spline Method for the Solution of Problems in Calculus of Variations

**Authors:**
M. Zarebnia,
M. Hoshyar,
M. Sedaghati

**Abstract:**

**Keywords:**
Calculus of variation; Non-polynomial spline functions; Numerical method

##### 9513 On the Efficiency of Five Step Approximation Method for the Solution of General Third Order Ordinary Differential Equations

**Authors:**
N. M. Kamoh,
M. C. Soomiyol

**Abstract:**

In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

**Keywords:**
Shifted Legendre polynomials,
third order block method,
discrete method,
convergent.

##### 9512 Solution of Nonlinear Second-Order Pantograph Equations via Differential Transformation Method

**Authors:**
Nemat Abazari,
Reza Abazari

**Abstract:**

In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.

**Keywords:**
Nonlinear multi-pantograph equation,
delay differential equation,
differential transformation method,
proportional delay conditions,
closed form solution.

##### 9511 Numerical Treatment of Block Method for the Solution of Ordinary Differential Equations

**Authors:**
A. M. Sagir

**Abstract:**

Discrete linear multistep block method of uniform order for the solution of first order initial value problems (IVPs) in ordinary differential equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

**Keywords:**
Block Method,
First Order Ordinary Differential Equations,
Hybrid,
Self starting.

##### 9510 A Collusion-Resistant Distributed Signature Delegation Based on Anonymous Mobile Agent

**Authors:**
Omaima Bamasak

**Abstract:**

**Keywords:**
Anonymous signature delegation,
collusion resistance,
e-commerce fairness,
mobile agent security.

##### 9509 Probabilistic Approach as a Method Used in the Solution of Engineering Design for Biomechanics and Mining

**Authors:**
Karel Frydrýšek

**Abstract:**

**Keywords:**
probabilistic approach,
engineering design,
traumatology,
rock mechanics

##### 9508 An Iterative Method for the Least-squares Symmetric Solution of AXB+CYD=F and its Application

**Authors:**
Minghui Wang

**Abstract:**

Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.

**Keywords:**
Matrix equation,
bisymmetric matrix,
least squares problem,
like-minimum norm,
iterative algorithm.

##### 9507 A Localized Interpolation Method Using Radial Basis Functions

**Authors:**
Mehdi Tatari

**Abstract:**

Finding the interpolation function of a given set of nodes is an important problem in scientific computing. In this work a kind of localization is introduced using the radial basis functions which finds a sufficiently smooth solution without consuming large amount of time and computer memory. Some examples will be presented to show the efficiency of the new method.

**Keywords:**
Radial basis functions,
local interpolation method,
closed form solution.

##### 9506 On the Approximate Solution of Continuous Coefficients for Solving Third Order Ordinary Differential Equations

**Authors:**
A. M. Sagir

**Abstract:**

This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y_{0}, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

**Keywords:**
Block Method,
Hybrid,
Linear Multistep,
Self starting,
Third Order Ordinary Differential Equations.

##### 9505 Significance of Splitting Method in Non-linear Grid system for the Solution of Navier-Stokes Equation

**Abstract:**

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed 'Non-linear grid system' is presented. The linear terms in Navier-Stokes equation are solved by Crank- Nicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Splitting method as pressure-velocity solver of higher efficiency with the advantage of consuming Non-linear grid system which produce more accurate results in relatively equal number of grid points as compared to Cartesian grid. The validation of Splitting method as a solution of Navier-Stokes equation in Nonlinear grid system is done by comparison with the benchmark results for lid driven cavity flow by Ghia and some case studies including Backward Facing Step Flow Problem.

**Keywords:**
Navier-Stokes,
'Non-linear grid system',
Splitting method.

##### 9504 On the Approximate Solution of a Nonlinear Singular Integral Equation

**Authors:**
Nizami Mustafa,
C. Ardil

**Abstract:**

In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.

**Keywords:**
Approximate solution,
Fixed-point principle,
Nonlinear singular integral equations,
Vekua integral operator

##### 9503 Method for Solving Fully Fuzzy Assignment Problems Using Triangular Fuzzy Numbers

**Authors:**
Amit Kumar,
Anila Gupta,
Amarpreet Kaur

**Abstract:**

In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy assignment problems by representing all the parameters as triangular fuzzy numbers. The advantages of the pro-posed method are also discussed. To illustrate the proposed method a fuzzy assignment problem is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy assignment problems occurring in real life situations.

**Keywords:**
Fuzzy assignment problem,
Ranking function,
Triangular fuzzy numbers.

##### 9502 Septic B-Spline Collocation Method for Numerical Solution of the Kuramoto-Sivashinsky Equation

**Authors:**
M. Zarebnia,
R. Parvaz

**Abstract:**

In this paper the Kuramoto-Sivashinsky equation is solved numerically by collocation method. The solution is approximated as a linear combination of septic B-spline functions. Applying the Von-Neumann stability analysis technique, we show that the method is unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The global relative error and L∞ in the solutions show the efficiency of the method computationally.

**Keywords:**
Kuramoto-Sivashinsky equation,
Septic B-spline,
Collocation
method,
Finite difference.